A girl start at A and walks 2km south to B. she then walks 3km west to C. find the distance and bearing of C from A
Looks like good ol' Pythagoras to me.
Use basic trig to find the angle.
Bearing is 236
Distance is 236
To find the distance and bearing from point A to point C, we can use the concepts of vector addition and trigonometry.
First, let's visualize the problem on a coordinate plane. Assume A is at the origin (0,0) of the plane.
The girl walks 2 km south, so the position of point B is (0, -2).
Next, she walks 3 km west, so the position of point C, relative to B, is (-3, -2).
To find the position of point C from point A, we need to combine these displacements by adding their respective coordinates.
Coordinates of C = Coordinates of A + Coordinates of B + Coordinates of C relative to B
Coordinates of C = (0, 0) + (0, -2) + (-3, -2)
= (0 + 0 + (-3), 0 + (-2) + (-2))
= (-3, -4)
So, the position of point C is (-3, -4).
To find the distance between points A and C, we can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Distance = sqrt((-3 - 0)^2 + (-4 - 0)^2)
= sqrt((-3)^2 + (-4)^2)
= sqrt(9 + 16)
= sqrt(25)
= 5 km
Hence, the distance of point C from point A is 5 km.
To find the bearing of C from A, we can use trigonometric functions.
Bearing = atan(dy/dx)
where dy = change in y-coordinate and dx = change in x-coordinate.
dy = -4 - 0 = -4
dx = -3 - 0 = -3
Bearing = atan(-4/-3) (using the arctan function)
= atan(4/3)
≈ 53.13°
Therefore, the bearing of point C from point A is approximately 53.13°.